What units are used for coordinates in geographic and projected coordinate systems?
A geographic projection will always be in degrees (or possibly radians) (the distinction between decimal and dms is one of formatting).
A projected crs can be in any units the designer wants, often meters or some kind of feet but I have seen "German Legal Metres", chains and many other weird options.
Geographic coordinates use angular units -- usually decimal degrees (DD), degrees and decimal minutes (DM), or degrees, minutes and seconds (DMS).
Projected coordinates use common linear units, typically meters or feet.
Note that different GIS standards will also specify how these different units are formatted. Some may be formatted for easy human readability, some for machine readability.
Note also that – unless you're restricted to using a fixed number of decimals – precision is a separate issue from units. More figures allow greater precision.
Pulling directly from ESRI's literature:
In a GCS: Yes, you are correct. "A point is referenced by its longitude and latitude values. Longitude and latitude are angles measured from the earth's centre to a point on the earth's surface." This could be in DMS format or decimal degrees.
In a PCS: The units of measurements vary, but Feet and Meters are common units as they are not often measured from the prime-meridian. "Each map projection has a set of parameters that you must define." This allows for a more targeted projection depending on the mapped area.